Some years ago I had a Y test done by Genographic and it was placed in the Dawson DNA database and the Ulster database both now hosted by Familytreedna.com I think. In those days (2007) only 12 markers were tested, although I understand that, providing the sample has not degraded, you can have it extended for ££. I had one other Irish Dawson contact me who reckoned we had a common ancestor within the last 700 years!
More recently I had an Ancestry DNA autosomal test done. This has confirmed links with many Irish and other families back to the late 17, early 1800s but not proved or disproved links with other Dawson Irish families from earlier times.
The autosomal test definitely has extended the number of cousins I knew about, but rather by delineating descendants rather than new branches.